Let f: M ---> N be a R module homomorphism

P and Q are submodules of M and N respectively.

Show that:

(i) f(P) ={ f(p): p belongs to P} is a submodule of N

(ii) f^(-1)(Q) ={ m in M: f(m) belongs to Q} is a submodule of M

(iii) What are f(M) and f^(-1)(0)?

I have already proved part (i) and (ii)

My problem is part (iii). I don't know how to do it, it looks easy but I think it is a trick question. So, I have to bother you to help me on part(iii)

Thank you in advanced